A multiscale correction method for local singular perturbations of the boundary
In this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution u of a second order elliptic equation posed in the perturbed domain with respect to the size parameter of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of u based on a multiscale superposition of the unperturbed solution and a profile defined in a model...